Bounds for the First Eigenvalue of (-Δ-R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-\varDelta -R)$$\end{document} Under the Ricci Flow on Bianchi Classes

被引：0
作者：
Fereshteh Korouki
Asadollah Razavi
机构：
[1] Shahid Bahonar University of Kerman,
来源：
Bulletin of the Brazilian Mathematical Society, New Series | 2020年 / 51卷 / 2期
关键词：
Eigenvalue; Ricci flow; Laplacian-type operator; Bianchi classes; 53C44;
D O I：
10.1007/s00574-019-00167-8
中图分类号：
学科分类号：
摘要：
In this paper, we analyse behavior of the first eigenvalue of the operator -Δ-R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\varDelta -R$$\end{document} on locally homogeneous closed 3-manifolds along the normalized Ricci flow, moreover in each Bianchi class we find bounds for the corresponding eigenvalues.
引用
收藏
页码：641 / 651
页数：10
相关论文
共 25 条
[1]  
Cao X(2007)Eigenvalues of Math. Ann. 2 435-441
[2]  
Cao X(2008) on manifolds with nonnegative curvature operator Proc. Am. Math. Soc. 11 4075-4078
[3]  
Cao X(2012)First eigenvalues of geometric operators under the Ricci flow Math. Ann. 354 451-463
[4]  
Hou S(2018)Estimate and monotonicity of the first eigenvalue under the Ricci flow Pac. J. Math. 296 1-20
[5]  
Ling J(1980)Monotonicity of eigenvalues of geometric operators along the Ricci–Bourguignon flow Phys. Rev. Lett 45 1057-30
[6]  
Chen B(1985)Nonlinear models in two+epsilon dimensions Ann. Phys. 163 318-306
[7]  
He Q(2013)Nonlinear models in two+epsilon dimensions Balkan J. Geom. Appl 2 20-6707
[8]  
Zeng F(1982)Ricci flow and the manifold of Riemannian metrics J. Differ. Geom. 17 255-594
[9]  
Friedan D(2006)Three-manifolds with positive Ricci curvature Class. Quant. Grav. 23 6683-1194
[10]  
Friedan D(2017)Ricci flow and black holes (Chinese) Acta Math. Sinica (Chin. Ser.) 60 583-741
123